Using a software package with big integer arithmetic support $($e$.$g$.$ Maple, Sage, Python$/$NumPy$,$

C$/$GMP$)$ develop a program to compute a discrete logarithm in Z$?$

p using Baby Step$-$Giant Step

Algorithm. You may use the large number arithmetic functions including modular exponentiation;

however you are $($obviously$)$ not allowed to use built$-$in discrete logarithm functions.

Find the discrete logarithm x $=$ log mod p for

$($a$)(40$ bits$)$ p $=2199023255867,$ $=3,$ and $=1228035139812.$

$($b$)(60$ bits$)$ p $=2305843009213699919,$ $=3$ and $=259893785866906004.$

$($c$)$ Bonus: $(80$ bits$)$ p $=2417851639229258349415043,$ $=3,$ and $=1007149824486452497234736.$

Include your implementation in your answer. For each case indicate how much time was spent

to complete the attack. Also indicate the platform information $($MHz speed, memory, chip type,

number of machines if you are running parallel threads etc.$).$